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A note on inverse results of random walks in abelian groups

Jake Koenig, Hoi H. Nguyen and Amanda Pan

Vol. 13 (2024), No. 1, 67–92
DOI: 10.2140/cnt.2024.13.67
Abstract

We give various near-optimal characterizations of random walks over finite abelian groups with large maximum discrepancy from the uniform measure. We also provide several interesting connections to existing results in the literature.

Keywords
Littlewood–Offord, anticoncentration, inverse problems
Mathematical Subject Classification
Primary: 11B25, 60B15
Milestones
Received: 21 August 2023
Revised: 31 December 2023
Accepted: 16 January 2024
Published: 13 March 2024
Authors
Jake Koenig
The Ohio State University
Columbus, OH
United States
Hoi H. Nguyen
Department of Mathematics
The Ohio State University
Columbus, OH
United States
Amanda Pan
Department of Mathematics
The Ohio State University
Columbus, OH
United States